Avoid any cotton like the plague, including your boxers, briefs, thongs or whatever you wear as underwear. Cotton soaks up your sweat and stays wet. On the mountain wet clothes = you feeling fucking cold. Therefore make sure whatever you wear is made of synthetic materials, e.g. polyester.

e.g. Burton make a range of 100% synthetic first and second layers. I wear that stuff and find it's very good quality.

I'm a cheap ass and it is just fucking polyester. Not some special material. That is why I use the $9 per piece Starter stuff from Walmart. If it is colder then I'll use Omni-wool that is $15 per piece at Sams Club. If it is really cold I'll use the Starter stuff and put my Old Navy fleece on. The expensive Smartwool/Under Armor/Patagonia is high quality but I don't think they are worth the premium.

In December in Aspen, is a single long-sleeve base layer sufficient for snowboarding or should I really be wearing an additional layer between the long-sleeve t-shirt and the waterproof jacket?

I hope when you say T-shirt you mean polyester T-shirt.

And the answer to your question is no, the single layer will not be sufficient. You will need a second layer - a hoodie, windstopper or fleece - again one that is made out of synthetic, breathable material.

There are no second layers on the legs as far as I know so just get a solid warm first layer down there.

Why does Burton offer so many pants options for the first layer? I could understand - lightweight, midweight and extra-warm - but 10 options seems excessive.

I haven't checked the link you added but Burton have at least 2 or 3 different clothing lines. These lines are supposed to differ in the quality of the materials, design, etc. So, take 10 base layer pants and divide them into 3 lines and you get 3 base layer pants per line. Then you can divide each line into light, medium, thick and on top of that you might get some extra models because of consumer preferences for different designs etc.

And the answer to your question is no, the single layer will not be sufficient. You will need a second layer - a hoodie, windstopper or fleece - again one that is made out of synthetic, breathable material.

There are no second layers on the legs as far as I know so just get a solid warm first layer down there.

It depends if your jacket is insulated or not. If it is, you might not need another layer. If it's only lightly insulated or it's just a shell, you'll definitely want something else.